Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries. The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is de-veloped by employing image-well theory with the superposition principle, of which the non-Darcian effect is characterized by Izbash' s equation. The solutions are derived by Boltzmann and dimensionless trans-formations. Then, the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution. The results show that the aquifer boundaries have non-negligible effects on pumping, and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping. The higher the degree of non-Darcian, the smaller the drawdown.